Subdivision-Based Mesh Convolution Networks

TL;DR

SubdivNet introduces a novel CNN framework for 3D meshes using subdivision surface hierarchies, enabling effective local feature aggregation and adaptation of 2D CNN architectures to irregular mesh data.

Contribution

It proposes a mesh convolution operator and a multi-resolution hierarchy that allow standard CNN concepts to be applied directly to 3D triangle meshes with Loop subdivision connectivity.

Findings

Effective local feature aggregation on meshes.

Supports standard CNN architectures on 3D meshes.

Demonstrates efficiency and versatility across applications.

Abstract

Convolutional neural networks (CNNs) have made great breakthroughs in 2D computer vision. However, their irregular structure makes it hard to harness the potential of CNNs directly on meshes. A subdivision surface provides a hierarchical multi-resolution structure, in which each face in a closed 2-manifold triangle mesh is exactly adjacent to three faces. Motivated by these two observations, this paper presents SubdivNet, an innovative and versatile CNN framework for 3D triangle meshes with Loop subdivision sequence connectivity. Making an analogy between mesh faces and pixels in a 2D image allows us to present a mesh convolution operator to aggregate local features from nearby faces. By exploiting face neighborhoods, this convolution can support standard 2D convolutional network concepts, e.g. variable kernel size, stride, and dilation. Based on the multi-resolution hierarchy, we make use of pooling layers which uniformly merge four faces into one and an upsampling method which splits one face into four. Thereby, many popular 2D CNN architectures can be easily adapted to process 3D meshes. Meshes with arbitrary connectivity can be remeshed to have Loop subdivision sequence connectivity via self-parameterization, making SubdivNet a general approach. Extensive evaluation and various applications demonstrate SubdivNet's effectiveness and efficiency.